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From: JW on 11 Aug 2010 19:43
This will probably be considered part of a few Univariate Optimisation
Questions.
Unfortunately my companies SAS licence does not include Enterprise
Miner or similar.

I am trying to understand how I can implement a recursive algorthim
using Base SAS.
I have done a great deal of reading (Customise BAse SAS Implemented
solvers being a good start).

I have a function derived from a logistic regression
FX = 3 - 0.2*log(x) - 0.35*x/100 + 0.14*Max(age-25)

x here is a price of the good and I calculate the probability of
purchase e(FX)/ (1+e(FX)) and an Expected Profit.

I now with to calculate the point where the Expected Profit is
maximized.

Now I can do this easily in Excel using the solver function, however I
wish to use SAS to do this somehow and then be able to extend it for
multiple profiles of age.

Unfortunately my attempts to extend my understanding of Macro's has
thus far been less than successful.
I have come across Brent's method which I believe is suitable for this
type of problem.

I have written the following based on what I thought (generously
relying on the above paper using the secant method) may just get me
there (however it doesn't work). It is perhaps a sign my thought
process isn't right.

This attempts to translate Brent's Method from Maxima & Fortran to SAS
based on what I found on the internet (www.netlib.org/go/
zeroin.fmin.f).

%macro zBrent(eqtn,x1,x2,eps);
*%local = root;
%let ITMAX = 100;
%let eps = 3.0E-8;
%let FX = 3 + -0.20*log(x)+-0.35*(x)/100 +0.14*(Max(age-16,0));
%let FXH = 3 + -0.20*log(x+0.01)+-0.35*(x+0.01)/100
+0.14*(Max(age-16,0));16,0));
%let ELAS = ((FXH-FX)/0.01)*(x)+1+exp(FX); (This being the elasticity
or 1st derivative of my Profit Function in a generic form usually you
would set this to 0 to maximize Profit).
%let eqtn2=%scan(&eqtn,1,"=");
%let eqtn3=%scan(&eqtn,2,"=");
%let eqt=%str(y=&eqtn2-&eqtn3;);

data OPT_Trial;
flag =0;
x= &x1;
&eqt; y1=y;
x = &x2;
&eqt; y2=y;
x = &x2;
&eqt; y3=y;

if y1>0 and y2>0 then do; put "No root within these borders"; end;
else if y1<0 and y2<0 then do; put "No root within these borders";
end;
else do until (flag =1);
do j = 1 to ITMAX;
if y2 > 0 and y3>0 then do;
x5=x4=x2-x1;
end;

else if y2<0 and y3<0 then do;
x5=x4=x2-x1;
end;

else if abs(y3) < abs(y2) then do;
x1 = x2;
x2 = x3;
x3 = x1;
y1 = y2;
y2 = y3;
y3 = y1;
end;

else if abs(y3) > abs(y2) then do;
tol1 = 2*EPS*abs(y2) + 0.5*tol;
xm = 0.5*(x3-x2);


if abs(xm) <= tol1 then root = x2;
if y2 = 0 then root =x2;
end;

if abs(x5) >= tol1 and abs(y1)> abs (y2)
then do s = y2/y1;
if x1 =x3 then do;

p = 2*xm*s;
q = 1-s;
end;
else if x1 ne x3 then do;
q = y1/y3;
r=y2/y3;
p = s*(2*xm*q*(q-r)-(b-a)*(r-1));
q = (q-1)*(r-1)*(s-1);
end;

if p < 0 then do
p = -p;
end;

if p >0 then do;
q = -q;
p =abs(p);
min1 = 3*xm*q-abs(tol1*q);
min2 = abs(e*q);

if 2*p < min1 then do;
e=d;
d=p/q;
end;

if p < Min2 then do;
e=d;
d=p/q;
end;

else do;
d=xm;
e=d;
end;

if abs(x5) < tol1 and abs(y1)> abs (y2) then do;
d=xm;
e=d;
end;
if abs(x5) >= tol1 and abs(y1)=< abs (y2) then do;
d=xm;
e=d;
end;
if abs(x5) < tol1 and abs(y1)=< abs (y2) then do;
d=xm;
e=d;
end;

x1 = x2;
y1 = y2;
if abs(x4) > tol1) then do;
x2=x2+x4;
x = &x2;
y2=y;
end;
if abs(x4) <= tol1) then do;
x2 = &eqt
else b = b+tol1;
x = &x2;
y2=y;
end;

end;
run;
%mend zBrent(ELAS=0,1,1000000,eps);

I wanted to find out whether any other SAS users have experience with
this type of problem and whether they had solutions. I don't believe
there is any hurry to upgrade our license in case this is basic thing
in Enterprise Miner or other SAS addon so I am restricted to
Enterprise 4.2 functions or code.

SAS Techncial help wasn't that useful recommending PROC Loess which
from what I understand is an alternative regression function.

With regards

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